Karthus is a fragile mage with high damage output and different playstiles depending on which ability is used more often

Probably y most of you are here for

Dorans ring can also be used to start but sell it late game
Upgrade to tear of the goddess fast to start increasing mana
Rabadon, tome or will can be bought in any way possible

Other possibilities instead of revolver
i use revolver for spell vamp but some options are
rod of ages: since i kamikaze this is a waste for me
lich bane is good since you spam spells (lay waste)
Zhonyas can be good with defile

9/0/21 i prefer for karthus to give him some spell vamp, mana and cdr and hes too squishy for 0/9/21

i start with lay waste for early harrasment. the rest is up to you but leave wall of pain for last
try to give lay waste a higher lvl than defile if you use it alot or vice wersa

take mid and harrass with lay waste from afar
careful if fighting a high range champ
when you feel you have an advantage attack and get close with defile and spam lay waste
remeber lay waste has a higher range than defile

tell everyone wehn your ulti is ready and DONT KS use it on runners
if you ks the team will hate you and not help you plus you wont have it if you need it

when laning stops harras the enemies from afar and dont rush in first

1: harrasement remember lay waste deals double damage if it hits 1 target
2: if want to try to be risky kamikaze and kill them with passive
3: take not of any enemies with heals, banshees and hourglasses
4: when fleeing and chasing turn on defile to feel like chuck norris
5: learn to use the wall to help team and yourself chase, run and reduce mage res
6: Spam 1 to use it as auto attack

i go with the classic ignite flash or exhaust flash or exhasut flash is good too

marks and glyphs and seals are the same for most mages flat ap runes quints are best but it is possible to use more spell vamp quints

harrass with q than use w to get close and use e than r on any runners

when fleeing use e and w and if oyur gonna die get close and q

note this is my first guide and comment any tips
have fun and dont feed, ks or make mages look bad